Resistance calculation of three-dimensional triangular and hexagonal prism lattices

Owaidat, M. Q.; Asad, Jihad

doi:10.1140/epjp/i2016-16309-x

Cited by 32 publications

(32 citation statements)

References 35 publications

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“…Later, Green's function was applied in literatures. [ 6,7 ] In order to solve the equivalent resistance of finite resistor networks, Wu established Laplacian matrix theory [ 8 ] for the study of resistor networks and gave the equivalent resistance of various types of resistor networks. The Laplacian matrix method has been widely applied; for example, literature [ 9 ] studied the trapezoidal Möbius band network using the Laplacian matrix method, and literature [ 10 ] studied the cobweb network by the Laplacian matrix method, etc.…”

Section: Introductionmentioning

confidence: 99%

“…Later, Green's function was applied in literatures. [6,7] In order to solve the equivalent resistance of finite resistor networks, Wu established Laplacian matrix theory [8] for the study of resistor resistor network model, set up the network with resistors of r a , r c , and r along the horizontal direction, and the vertical resistance is r 0 , and the horizontal grid number is n. Let the equivalent resistance between nodes A 0 ,B 0, and C 0 be R ac (n), R ab (n) , and R bc (n). In this paper, three equivalent resistance analytical expressions are obtained as follows…”

Section: Introductionmentioning

confidence: 99%

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Resistance Theory of General 2 × n Resistor Networks

Zhang

Huang

Chen

et al. 2021

Advcd Theory and Sims

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Here the problem of equivalent resistance of general 2 × n‐order resistor networks with four different resistor parameters is investigated, and innovations in theory and method are made. Here, the second‐order matrix equation model and boundary condition equation model are established by the RT‐I technique (recursion–transform theory based on current parameters), and the general solution and the special solution of the matrix equation are given by using the matrix transformation method. The current distribution law in the circuit is obtained, and three equivalent resistance formulas of general 2×n‐order resistor networks are obtained. Finally, by analyzing and discussing the special case of the conclusion, the relationship between different resistances is obtained, and the results are compared with those of other literatures.

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Section: Introductionmentioning

confidence: 99%

“…Later, Green's function was applied in literatures. [6,7] In order to solve the equivalent resistance of finite resistor networks, Wu established Laplacian matrix theory [8] for the study of resistor resistor network model, set up the network with resistors of r a , r c , and r along the horizontal direction, and the vertical resistance is r 0 , and the horizontal grid number is n. Let the equivalent resistance between nodes A 0 ,B 0, and C 0 be R ac (n), R ab (n) , and R bc (n). In this paper, three equivalent resistance analytical expressions are obtained as follows…”

Section: Introductionmentioning

confidence: 99%

Resistance Theory of General 2 × n Resistor Networks

Zhang

Huang

Chen

et al. 2021

Advcd Theory and Sims

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“…The Green function method is formulated by Cersti in 2000 to compute the equivalent resistance of diverse infinite resistor networks 13,14 . It is developed, lately, by J. Asad et al in References 15,16, Hijjawi et al in Reference 17 and Owaidat et al in References 18‐20 for studying many circuit designs such as the cubic, the triangular and the honeycomb lattice.…”

Section: Introductionmentioning

confidence: 99%

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

Ammar¹,

Vincent

2020

Int J Numerical Modelling

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The paper presents a theoretical study of a rectangular electrical network built on two layers. First, the auxiliary source notion is introduced for characterizing the potential difference over each electrical element, then the mathematical formalism of the Wave Concept Iterative Process method is developed and adopted to the studied circuit. The used method is based on the concept of the incident and reflected waves which are defined from the current and voltage at each branch of the circuit. Two relations connecting the waves are established into two definition domains: a spectral-domain using the Kirchhoff laws and the auxiliary source connections and, another spatial defining the boundary conditions and the circuit design. Hence a two equations system is obtained and it is resolved by an iterative process, the transition between the two domains is ensured by the fast Fourier transform and its inverse. Moreover, the equivalent impedance between the feeding source and the nodes of the bottom layer has been calculated. Among the numerical simulation methods, this method has demonstrated its performances for analyzing various designs of the networks including RL, RC and RLC circuits excited by a lumped voltage source. The effect of the circuit parameters on the electrical currents and equivalent impedance has been studied.

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“…the current law and the voltage law). Since then, many resistor network models have been investigated in previous research [1][2][3][4][5][6][7][8][9][10]. Modern science has made great progress thanks to the development and application of circuit theory.…”

Section: Introductionmentioning

confidence: 99%

“…Infinite networks consisting of either identical resistors or identical capacitors have been the subject of much research effort for a long time. Three methods and techniques that have been developed are mainstream in investigating the infinite resistor networks, including the current distribution method [1], the lattice Green's function (LGF) method [3][4][5][6][7][8][9][10] and the random walk method [11,12]. The LGF method is important because it enables us to study infinite perfect networks in addition to perturbed infinite networks, as one can see in the previous works carried out.…”

Section: Introductionmentioning

confidence: 99%

Electrical characteristics of the 2 × n and □ × n circuit network

2019

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This paper presents two new fundamentals of the 2×n and ,×n circuit network. The results of a plane 2×n resistor network can be applied to a ,×n circuit network, which has not been studied before. We first study the 2×n resistor network by modeling a differential equation and obtain two equivalent resistances between two arbitrary nodes of the 2×n network. Next, the ,×n cube network is transformed to the 2×n plane network equivalently to achieve two resistance formulae between two arbitrary nodes of the ,×n cube network. By applying the resistance results to the ,×n LC cube network, the complex impedance characteristics of the LC network, which includes oscillation characteristics and resonance properties, are discovered.

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Resistance calculation of three-dimensional triangular and hexagonal prism lattices

Cited by 32 publications

References 35 publications

Resistance Theory of General 2 × n Resistor Networks

Resistance Theory of General 2 × n Resistor Networks

Design and analysis of two layers RLC network of rectangular topology by wave concept iterative process method

Electrical characteristics of the 2 × n and □ × n circuit network

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